Counting and selecting at random bipartite graphs with fixed degrees
Counting biorders.
Counting bordered partial words by critical positions.
Counting colorings on varieties.
We present a combinatorial mechanism for counting certain objects associated to a variety over a finite field. The basic example is that of counting conjugacy classes of the general linear group. We discuss how the method applies to counting these and also to counting unipotent matrices and pairs of commuting matrices.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
Counting -polytopes with vertices.
Counting defective parking functions.
Counting fixed-height tatami tilings.
Counting forests by descents and leaves.
Counting graphs with different numbers of spanning trees through the counting of prime partitions
Let be the set of all integers such that there exists a connected graph on vertices with precisely spanning trees. It was shown by Sedláček that...
Counting horizontally convex polyominoes.
Counting Lamé differential operators
Counting lattice paths by Narayana polynomials.
Counting Maximal Distance-Independent Sets in Grid Graphs
Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any ℓ ∈ N, maximal distance-ℓ independent (or simply: maximal ℓ-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied
Counting multiderangements by excedances.
Counting nondecreasing integer sequences that Lie below a barrier.
Counting nonintersecting lattice paths with turns.
Counting non-isomorphic maximal independent sets of the -cycle graph.
Counting occurrences of 132 in an even permutation.
Counting ordered patterns in words generated by morphisms.
Counting paths between points on a circle
The paper deals with counting sets of given magnitude whose elements are self-avoiding paths with nodes from a fixed set of points on a circle. Some of the obtained formulae provide new properties of entries in ``The On-line Encyclopaedia of Integer Sequences", while others generate new entries therein.